Continuous Model Theory

Limit models in metric abstract elementary classes: the categorical case

“…One of the four kinds (kind III: existentially closed models of a universal theory with the JEP) included a particular case (stability theory for normed spaces and for Banach spaces, only hinted at in [11]). A long array of results, starting with earlier work by Chang and Keisler [4], with crucial ideas from Henson and Iovino [8], finally converged in the monograph [3] that settled the foundation of first order metric continuous model theory. Our work aims at wider classes of models, and builds on a combination of abstract elementary classes with more purely metric continuous logic constructions.…”

Model theory of operator algebras III: elementary equivalence and II1factors

“…This is a 'continuous model theory', meaning that the truth value of a formula is taken from a bounded real interval (possibly depending on the formula) instead of the discrete set {T, F }. The continuity of the range of the truth variable is of course not a new idea in logic [7] or even in model theory [27], but the syntax in this approach is particularly clear and flexible.…”

Cardinals in Isabelle/HOL

“…In the literature, Zorn seems to be generally preferred by algebraists [23], while transfinite recursion/induction is a speciality of logicians [3]. For this particular instance, the latter approach felt more intuitive and (its informal version) was easier to discover and formulate.…”